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Simplifying 0.4(z + -0.5) = -0.1(z + 12) Reorder the terms: 0.4(-0.5 + z) = -0.1(z + 12) (-0.5 * 0.4 + z * 0.4) = -0.1(z + 12) (-0.2 + 0.4z) = -0.1(z + 12) Reorder the terms: -0.2 + 0.4z = -0.1(12 + z) -0.2 + 0.4z = (12 * -0.1 + z * -0.1) -0.2 + 0.4z = (-1.2 + -0.1z) Solving -0.2 + 0.4z = -1.2 + -0.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.1z' to each side of the equation. -0.2 + 0.4z + 0.1z = -1.2 + -0.1z + 0.1z Combine like terms: 0.4z + 0.1z = 0.5z -0.2 + 0.5z = -1.2 + -0.1z + 0.1z Combine like terms: -0.1z + 0.1z = 0.0 -0.2 + 0.5z = -1.2 + 0.0 -0.2 + 0.5z = -1.2 Add '0.2' to each side of the equation. -0.2 + 0.2 + 0.5z = -1.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.5z = -1.2 + 0.2 0.5z = -1.2 + 0.2 Combine like terms: -1.2 + 0.2 = -1 0.5z = -1 Divide each side by '0.5'. z = -2 Simplifying z = -2
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